1. Hello, I've just finished two optimization problems for my calculus class. I would really appreciate it if someone could check my work for me.

2.

3. I haven't checked every step, but the setup and overall methodology looks fine to me. Hint on Number 2: maximize $d^2$. Then you don't have to bother with square roots.

4. 2.

$\displaystyle -\dfrac{1}{2x}x+3=x^2-1\Rightarrow x=\pm\sqrt\frac72$